Genius (42 page)

Where this image should have been, instead there was a void, as frothy and alive with possibility as the unquiet vacuum of the new physics. Unable to let their minds fix on even a provisional picture of quantum events, some physicists turned to a new kind of philosophizing, characterized by paradoxical thought experiments and arguments about
reality
,
consciousness
,
causality
, and
measurement
. Such arguments grew to form an indispensable part of the late twentieth century’s intellectual atmosphere; they trailed the rest of physics as a cloud of smoke and flotsam trails a convoy. They were provocative and irresolvable. The paper of Einstein, Podolsky, and Rosen in 1935—the paper that provided the seventeen-year-old Schwinger with his first opportunity to impress Rabi—became an enduring example. It posed the case of two quantum systems—atoms, perhaps—linked by a particle interaction in their past but now separated by a great distance. The authors showed that the plain act of measuring one atom of this pair would affect what one could measure about the other atom, and the effect would be instantaneous—faster than light and thus retroactive, as it were. Einstein considered this a damning commentary on the laws of quantum mechanics. Bohr and younger theorists maintained a more sanguine attitude, noting that Einstein himself had already placed
past
and
distance
into the class of concepts about which one could no longer speak with comfortable, classical certainty. In the same vein was Schrödinger’s famous cat: a poor hypothetical animal sitting in a box with a vial of poisonous gas attached to a detector, its fate thus linked to that same quantum-mechanical event, the emission of a photon from an atom. Schrödinger’s point was that, while physicists now glibly calculated such events as probabilities—half yes and half no, perhaps—they still could not visualize a cat as anything but alive or dead.

Physicists made a nervous truce with their own inability to construct unambiguous mental models for events in the very small world. When they used such words as
wave
or
particle
—and they had to use both—there was a silent, disclaiming asterisk, as if to say:
not really
. As a consequence, they recognized that their profession’s relationship to reality had changed. Gone was the luxury of supposing that a single reality existed, that the human mind had reasonably clear access to it, and that the scientist could explain it. It was clear now that the scientist’s work product—a theory, a model—interpreted experience and construed experience in a way that was always provisional. Scientists relied on such models as intensely as someone crossing a darkened room relies on a conjured visual memory. Still, physicists now began to say explicitly that they were creating a language—as though they were more like literary critics than investigators. “It is wrong to think that the task of physics is to find out how nature is,” said Bohr. “Physics concerns only what we can
say
about nature.” This had always been true. Never before, though, had nature so pointedly rubbed physicists’ noses in it.

Yet in the long run most physicists could not eschew visualization. They found that they needed imagery. A certain kind of pragmatic, working theorist valued a style of thinking based on a kind of seeing and feeling. That was what
physical intuition
meant. Feynman said to Dyson, and Dyson agreed, that Einstein’s great work had sprung from physical intuition and that when Einstein stopped creating it was because “he stopped thinking in concrete physical images and became a manipulator of equations.” Intuition was not just visual but also auditory and kinesthetic. Those who watched Feynman in moments of intense concentration came away with a strong, even disturbing sense of the physicality of the process, as though his brain did not stop with the gray matter but extended through every muscle in his body. A Cornell dormitory neighbor opened Feynman’s door to find him rolling about on the floor beside his bed as he worked on a problem. When he was not rolling about, he was at least murmuring rhythmically or drumming with his fingertips. In part the process of scientific visualization is a process of putting oneself in nature: in an imagined beam of light, in a relativistic electron. As the historian of science Gerald Holton put it, “there is a mutual mapping of the mind … and of the laws of nature.” For Feynman it was a nature whose elements interacted with palpable, variegated, fluttering rhythms.

He thought about it himself. Once—uninterested though he was in fiction or poetry—he carefully copied out a verse fragment by Vladimir Nabokov: “Space is a swarming in the eyes; and time a singing in the ears.”

“Visualization—you keep repeating that,” he said to another historian, Silvan S. Schweber, who was trying to interview him.

What I am really trying to do is bring birth to clarity, which is really a half-assedly thought-out pictorial semi-vision thing. I would see the jiggle-jiggle-jiggle or the wiggle of the path. Even now when I talk about the influence functional, I see the coupling and I take this turn—like as if there was a big bag of stuff—and try to collect it away and to push it. It’s all visual. It’s hard to explain.

“In some ways you see the answer——?” asked Schweber.

——the character of the answer, absolutely. An inspired method of picturing, I guess. Ordinarily I try to get the pictures clearer, but in the end the mathematics can take over and be more efficient in communicating the idea of the picture.

In certain particular problems that I have done it was necessary to continue the development of the picture as the method before the mathematics could be really done.

The field itself presented the ultimate challenge. Feynman once told students, “I have no picture of this electromagnetic field that is in any sense accurate.” In seeking to analyze his own way of visualizing the unvisualizable he had learned an odd lesson. The mathematical symbols he used every day had become entangled with his physical sensations of motion, pressure, acceleration … Somehow he invested the abstract symbols with physical meaning, even as he gained control over his raw physical intuition by applying his knowledge of how the symbols could be manipulated.

When I start describing the magnetic field moving through space, I speak of the
E-
and
B-
fields and wave my arms and you may imagine that I can see them. I’ll tell you what I see. I see some kind of vague, shadowy, wiggling lines … and perhaps some of the lines have arrows on them—an arrow here or there which disappears when I look too closely… . I have a terrible confusion between the symbols I use to describe the objects and the objects themselves.

Yet he could not retreat into the mathematics alone. Mathematically the field was an array of numbers associated with every point in space. That, he told his students, he could not imagine at all.

Visualization did not have to mean diagrams. A complex, half-conscious, kinesthetic intuition about physics did not necessarily lend itself to translation into the form of a stick-figure drawing. Nor did a diagram necessarily express a physical picture. It could merely be a chart or a memory aid. At any rate diagrams had been rare in the literature of quantum physics. One typical example used a ladder of horizontal lines to represent the notion of energy levels in the atom:

The “quantum jump” visualized as a sort of ladder.

The quantum jump from one level down to another accompanied the emission of a photon; the absorption of a photon would bring a jump upward. No depiction of the photons appeared in these diagrams; nor in another, more awkward schematic for the same process.

Feynman never used such diagrams, but he often filled his note pages with drawings of a different sort, recalling the space-time paths that had been so crucial a feature of his Princeton work with Wheeler. He drew the paths of electrons as straight lines, moving across the page to represent motion through space and up the page to represent progress through time. At first he, too, left the emission of a photon out of his pictures: that event would appear as the deflection of an electron from one path to another. The absence of photons did reflect an implicit choice from among the available pictorial landscapes: Feynman was still thinking mainly in terms of electrons interacting with the electromagnetic field as a field, rather than with the field as incarnated in the form of particles, photons.

In mid-1947 friends of Feynman persuaded him—threats and cajoling were required—to write for publication the theoretical ideas they kept hearing him explain. When he finally did, he used no diagrams. The result was partly a reworking of his thesis, but it also showed the maturing and broadening of his command of the issues of quantum electrodynamics. He expressed the tenets of his new vision with an unabashed plainness. For some physicists this would be the most influential set of ideas Feynman ever published.

He said he had developed an alternative formulation of quantum mechanics to add to the pair of formulations produced two decades before by Schrödinger and Heisenberg. He defined the notion of a
probability amplitude for a space-time path
. In the classical world one could merely add probabilities: a batter’s on-base percentage is the 30 percent probability of a base hit plus the 10 percent probability of a base on balls plus the 5 percent probability of an error … In the quantum world probabilities were expressed as complex numbers, numbers with both a quantity and a phase, and these so-called
amplitudes
were squared to produce a probability. This was the mathematical procedure necessary to capture the wavelike aspects of particle behavior. Waves interfered with one another. They could enhance one another or cancel one another, depending on whether they were in or out of phase. Light could combine with light to produce darkness, alternating with bands of brightness, just as water waves combining in a lake could produce doubly deep troughs and high crests.

Feynman described for his readers what they already knew as the canonical thought experiment of quantum mechanics, the so-called two-slit experiment. For Niels Bohr it had illustrated the inescapable paradox of the wave-particle duality. A beam of electrons (for example) passes through two slits in a screen. A detector on the far side records their arrival. If the detector is sensitive enough, it will record individual events, like bullets striking; it might be designed to click as a Geiger counter clicks. But a peculiar spatial pattern emerges: the probabilities of electrons arriving at different places vary in the distinct manner of diffraction, precisely as though waves were passing through the slit and interfering with one another. Particles or waves? Sealing the paradox, quantum mechanically, is a conclusion that one cannot escape: that each electron “sees,” or “knows about,” or somehow
goes through
both slits. Classically a particle would have to go through one slit or the other. Yet in this experiment, if the slits are alternately closed, so that one electron must go through A and the next through B, the interference pattern vanishes. If one tries to glimpse the particle as it passes through one slit or the other, perhaps by placing a detector at a slit, again one finds that the mere presence of the detector destroys the pattern.

Probability amplitudes were normally associated with the likelihood of a particle’s arriving at a certain place at a certain time. Feynman said he would associate the probability amplitude “with an entire motion of a particle”—with a path. He stated the central principle of his quantum mechanics:
The probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way.
These complex numbers, these amplitudes, were written in terms of the classical action; he showed how to calculate the action for each path as a certain integral. And he established that this peculiar approach was mathematically equivalent to the standard Schrödinger wave function, so different in spirit.

The central mystery of quantum mechanics—the one to which all others could ultimately be reduced.

A gun (obeying the classical laws) sprays bullets toward a target. First they must pass through a screen with two slits. The pattern they make shows how their
probability
of arrival varies from place to place. They are likeliest to strike directly behind one of the slits. The pattern happens to be simply the sum of the patterns for each slit considered separately: if half the bullets were fired with only the left slit open and then half were fired with just the right slit open, the result would be the same.